Method of single expression-advanced powerful tool for computer modelling of wavelength scale nonuniform frequency-selective 1D photonic structures

Abstract

Main principles of the method of single expression (MSE) for boundary problems solution in classical electrodynamics are presented. In the MSE the solution of the Helmholtz's equation is presented in the special form of a single expression. As a consequence, attained liberty from the obligation of the superposition principle permits to solve both linear and nonlinear problems with the same ease. In the MSE the Helmholtz's equation is reformulated to the set of first order differential equations and the boundary problem is solved numerically. Using the MSE steady-state boundary problems are investigated for wavelength scale multilayer and modulated 1D photonic structures including loss, amplification and nonuniformity evoked by intense electromagnetic field.